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Target point‐based path‐following controller for a car‐type vehicle using bounded controls
Author(s) -
Harmouche Mohamed,
Laghrouche Salah,
Chitour Yacine
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3225
Subject(s) - control theory (sociology) , controller (irrigation) , lipschitz continuity , exponential stability , bounded function , lyapunov stability , lyapunov function , trajectory , nonlinear system , stability theory , computer science , path (computing) , mathematics , control (management) , artificial intelligence , mathematical analysis , physics , quantum mechanics , astronomy , agronomy , biology , programming language
Summary In this paper, we have studied the control problem of target point‐based path following for car‐type vehicles. This special path‐following task arises from the needs of vision‐based guidance systems, where a given target point located ahead of the vehicle, in the visual range of the camera, must follow a specified path. A solution to this problem is developed through a nonlinear transformation of the path‐following problem into a reference trajectory tracking problem, by modeling the target point as a virtual vehicle. The use of target point complicates the control problem, as the development produces a first‐order nonlinear nonglobally Lipschitz differential equation with finite escape time. This problem is solved by using small control signals. Bounded feedback laws are designed to control the real vehicle's angular acceleration and the virtual vehicle's velocity, to achieve stability. The resulting controller is globally asymptotically stable with respect to the origin, the proof of which is derived from Lyapunov‐based arguments and a bootstrap argument. It is also shown that the use of exponentially convergent observers/differentiators does not affect the stability of the closed‐loop system. The effectiveness of this controller has been illustrated through simulations. Copyright © 2014 John Wiley & Sons, Ltd.